SOLUTION: Hi There were 150 people. The boys,girls and adults were in the ratio of 5 to 8 to 2 respectively. When some girls left the new ratio became 10 to 9 to 4 respectively. How many gi

Question 1193224: Hi
There were 150 people. The boys,girls and adults were in the ratio of 5 to 8 to 2 respectively. When some girls left the new ratio became 10 to 9 to 4 respectively. How many girls left the marathon.
Thanks
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
i get the following:

the ratio boys to girls to adults is equal to 5 to 8 to 2.
the total of this set is 15.
there is a total of 150 people.
the number of sets of 15 is therefore equal to 150/15 = 10.
from this, you get the number of boys is 50 and the number of girls is 80 and the number of adults is 10.

you get 50 boys plus 80 girls plus 20 adults = a total of 150.

you remove x number of girls from the group.

the ratio of boys to girls to adults becomes 10 to 9 to 4.

let x = the number of girls that were removed.

you get:
50 / (80 - x) = 10 / 9
cross multiply to get:
450 = 800 - 10x
solve for x to get:
x = (800 - 450) / 10 = 35

you also get:
(80 - x) / 20 = 9 / 4
cross multiply to get:
320 - 4x = 180
solve for x to get:
x = (320 - 180) / 4 = 35

looks like 35 girls were removed.

you started with 50 boys and 80 girls and 20 adults.
you ended up with 50 boys and 45 girls and 20 adults.

starting ratio of boys to girls was 50/80 = 5/8.
ending ratio of boys to girls was 50/45 = 10/9.

starting ratio of girls to adults was 80/20 = 8/2.
ending ratio of girls to adults was 45/20 = 9/4.

starting ratio was 5/8/2.
ending ratio was 10/9/4.

solution is 35 girls left the marathon.

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